'Last week we had a life.' Ukrainians criss-cross country for days in search of escape route

Romanian Red Cross workers hand out blankets to refugees from Ukraine who crossed the border at Sighetu Marmatiei, Romania, shortly before midnight on February 28.

Sighetu Marmatiei, Romania (CNN)Elena Holitsyna and her daughter, Valerie, were exhausted by the time they arrived in Sighetu Marmatiei, Romania, and were greeted by dozens of volunteers and a little girl handing out yellow tulips.

They had spent four days crisscrossing Ukraine, hoping to find safety, each day bringing with it more news of Russian soldiers advancing through their country. 
"Last week, we had a life. We had plans," the 39-year-old, dressed in a white coat stained from the arduous journey, said. "And now, our life is this," she said, sobbing amid her possessions -- the few pieces of luggage they'd packed in a rush to flee Kyiv. Valerie, 16, clutched the Ukulele she got just last week.
    The day before the Russian invasion, Holitsyna, a French teacher, was teaching vocabulary, while Valerie was planning to buy a gift for her half-sister's birthday. "She turned three yesterday," Valerie said. 
      Now they are hundreds of miles apart. Valerie's half-sister is staying with her mother in her maternal grandparents' village.
      Holitsyna's brother had driven them toward the border while her partner, a doctor at a Kyiv hospital, remained in the city to treat the wounded. "My heart is in two," broken, she said. "Part is with Valerie and part is with the man I love."
      Initially, Holitsyna's brother had headed for Lviv, she said, "but there are tens of thousands of people waiting" to cross into Poland, so they made no attempt to queue there, opting to drive to Romania instead. 
        "This isn't the first time this has happened, but it is the worst," Holitsyna said. 
        The family started a new life in Kyiv after being uprooted in 2014 when Russian-backed separatists occupied the Donbas region of eastern Ukraine, which was their home.
        Now, under a tent set up by volunteers, Holitsyna, Valerie and Holitsyna's 64-year-old father waited for a relative who relocated to Bulgaria in 2014, and who had been driving overnight to reach them in this hilly, sparsely-populated region.
        They are among the 677,000 people who have fled their homes in Ukraine in less than a week, according to the UNHCR, which fears it could become "Europe's largest refugee crisis this century."
        They are seeking refuge from the Russian invasion that has upended international politics and triggered the greatest security crisis in Europe since the Cold War
        UNHCR has issued an appeal for $1.7 billion USD in aid, estimating that 12 million people in Ukraine could be left in need of relief and protection, with a further four million expected to need help in neighboring countries. 
        Meanwhile, the UN says that at least 102 civilians have been killed across the country and 304 injured, though those figures are likely underestimated.
        As Ukraine's European neighbors pledged to welcome the country's citizens with open arms, many refugees first fled to Lviv, a large city just over two hours' drive from the Polish border. But Ukrainian-Polish border crossings have now become bottlenecked, with refugees reporting having to wait in seemingly endless lines in the freezing weather.
        Accounts such as these are forcing many of those desperate to get out to head south instead, including to Romania, the EU country with which Ukraine shares the longest border.